Mean Value Theorem

[MrCyborg29]

thank you for explaining open/closed interval

[Alicetalk]

photosynthesis, respiration, mean value theorem...khan academy is always there to help me when i need it (and thank god - my grade would have suffered greatly without it)

[Godamie]

Why can't teachers and textbooks just explain right on the spot with simple words instead of trying to make it sound all scholarly and beating around the bush?

[TerminatorSe7en]

Say the interval is [a,b], can C be equal to a? or just the open interval ( A point somewhere between a and b )?

[mariahphilmrazem]

you make my life so much easier you have no idea. my book makes no sense to me but you make it make sense. thank you so much!

[roneykaithpalmaria]

THIS CALLS FOR MAGENTA 

[GangstaReviewer]

hi, im a fellow youtuber and i think your channel is really awesome i subbed :)

[sanelijo2005]

yes i do believe it calls for magenta

[zayoob0524]

This calls for magenta!

[hmmmmm12]

You're great at explaining things, thanks a lot! 

[guitarlover113]

Dude honestly i say the government should just take all of their money towards improving education in America and just give it to you to make awesome videos.

Your the only teacher america needs.

[happy321hh]

Its funny how the ppl on you tube make you understand to much compared to shit teachers.

[uchihaevil2]

Thanks for the guide!!! It really helped me understand for my calculus class!!! XD

[sukki664]

Thanks so much!! U are a lifesaver :D

[zayoob0524]

I watch your lectures after every math lesson I learn...then I get it.

[jkidd55547]

i love u... nuff said...

[markustheaters]

thank you so much!

[avestak]

5 instructors who were never able to teach so clearly after 30 years, "disliked" it ! Lol

[luyanalina]

wow you made it SO CLEAR for me!! best tutor one could ever have!

[victorcg]

A Divine gift you've got there Sal, thank you so much

[deathmoonkiller]

I feels good after watching this, my lecturer definitely confused me everything about this.

[Oboeplayer511]

It's cool if you solve this for a general quadratic; Ax^2+Bx+C for the interval [h,k]

(A(h^2)+B(h)+C)-(A(k)^2+B(k)+C­))/(h-k)=2Ax+B (derivative of the general quadratic)

(A(h^2)-A(k)^2+B(h)-B(k))/(h-k­)=2Ax+B

(A(h^2-k^2)+B(h-k))/(h-k)=2Ax+­B

(A(h-k)(h+k)+B(h-k))/(h-k)=2Ax­+B

A(h+k)+B=2Ax+B

A(h+k)=2Ax

x=(h+k)/2

so the x-coordinate for any parabola where the average slope is equal to the slope of the derivative at the point is equal to the average of the endpoints of that interval...FASCINATING

[bobbyflaylover69]

@Oboeplayer511 you just made that up

[pthorn91]

I think this calls for magenta

[Joshua6Tube]

U r REALLY GOOD!!! Thanks cause i'm taking Calc 2 class in the fall semester, so i'm trying to study ahead,

THANKS ALOT though......and trust me u did great u were not confusing @ all

[ayulo1]

U r the best...not confusin at all

[hellnoid90]

teachers can learn a lot from you...

THANK YOU,honestly

[Joshida9]

everything makes sense now

[TyTimeIsAwesome]

thank you..so much.

[LuckynumberSlevin11]

Lehmans's terms King

[Ibahz]

i like your videos but you SAY INTUITION way too much

[xGore220]

thank you, your a lifesaver

[OZZl3]

I just noticed today according to "Calculus A Complete Course - Robert A. Adams (Sixth Editon)" page 129 that they say on a OPEN intervall not on a closed intervall, but maybe that doesn't matter?

[OZZl3]

@OZZl3 I saw now that it is:

"f is continuous on the closed, finite interval [a, b] and that it is diffrentiable on the open interval (a, b) ...."

[zero3609]

Sal.... You are AWESOME, thank you

[NatalyInsanity]

I LOVE the black background! I love not becomong blind while watching it at night xD



[BRESNYFUL]

OMG THANK YOU IM LIKE IN LOVE WITH YOU NOW...this was a big help.. im using ur channel to review for my ap calc test.

[pSychOAtDawn]

what happened to continuous but not differentiable example?

[ztpo]

easy to understand thanksssss

[revanxisxkool]

when he asked what differentiable meant, i answered him outloud as if he was sitting right here, by accident. hahaha

[matinaeau]

Yes need it for proofs!!!

[Seedofwinter]

One of these days you gonna blow my ears out, Sal. Jeez you cough loud.

But I am greatly appreciative of your jovial teaching methods. but fix the cough LOL

[JohnTheScienceGuy]

what happened to the example where it's continuous but not differentiable?

[desidork000]

how are you so good at using a mouse and neat i can't do that omg

[Seedofwinter]

@desidork000 LOL It's not a mouse, it's an electronic pen.

[friedduc]

@desidork000 He's actually using an electronic pen not a mouse.

[OZZl3]

This is great, I can really understand this, however we are asked to prove the mean value theorem with help from Rolle's theorem which we should also know. I've been looking at Rolle's theorem and seems quite straight farward but I'm still a bit puzzled as how these theorems correlate..

I'm doing a masters degree in Interactiondesign and I'm absolutely sure I will never have use for this in my future work :< My course responsible says that we are tough math just to think abstractly *sigh*

[desidork000]

you are fantastic.

[bothar54]

Brilliant!! THANK YOU SO SO MUCH! you are so easy to follow and clear.

God I soooo wish you were my lecturer! Thank you so much for posting these videos they are such a great help.

Would love if yo ucould do something similiar with Riemanns Criteria for integrability

[bothar54]

Brilliant!! THANK YOU SO SO MUCH! you are so easy to follow and clear.

God I soooo wish you were my lecturer! Thank you so much for posting these videos they are such a great help.

Would love if yo ucould do something similiar with Riemanns Criteria for integrability

[xxxsde]

hope i didnt confuse you??? hahaha..are you kidding me??

you just fucking saved my grade!!!

[Arelymelendez10]

i love his voice! idk but i think it makes the topics easier to understand :)

[KNMChannel]

4 people are in pre-calc

[Darkryers]

Grreat stuff! Thanks, very straightforward.

[RaniOfCoochNahi]

Thank you!! I like your statement that was something like 'it gives you something new to know about the world'. I really need to start approaching all my learning like this--to think "It's nice to understand another little bit of how the world works" instead of my usual, "ugh, maths" attitude. :)

[mssca]

THANK YOU SOOOOOOO MUCH.

[CryBaby82]

great help, thanks!

[xROFLawsonx]

Amazing! I didn't even realize this. Thanks.

[dawodchatha]

your amazing

[MrLmfao4u]

truust me u did not confuse us ;)

[cpcrasher]

Thanks man! awesome Vid

[NarutoOfThunderClan]

can you or do u already have a video about Rolle's theorem?

[zohaaa]

i dont even see the point of going to classes anymore. i just watch these videos and make sense out of my hwrk. salmman ur awesome!

[myqueensindel]

Uh Sal, can I like.... send you money or a bottle wine or something?

All your help does not deserve to go up rewarded, it just doesn't.

So if you ever want like a new iPod, a video game, a blow job, a box of cookies, just holler at me okay?

[KingRobbStark]

@myqueensindel Blowjob? Damn, maybe I should start uploading videos as well.

[DirrrtyDutchMTRFCKR]

@KingRobbStark It's a trap. It's a male.

[brHOLLAND]

I really could have used this channel earlier in the semester.

Ah well, better late than never.

Thanks!

[TheDennyvu]

I no totally dont pay attention to my teacher that makes no sense whatsoever, they way you explain this is just that much better

[1demp]

thats right in Khan we trust"preach!

[utkar1]

you are AWESOME..

but why are we studying this theorem..

if you could give some applications of it, that would make the existence of this theorem more sense.

Thanks :)

[emadrio]

Seriously, if you wrote a math book, I would easily pay 25% more for your book then the traditional math books I have to read. Thanks a bunch for posting

[semlan14]

awesome video!

[mollierdiag]

Very easy to follow and enjoyable to watch. Thank you.

[1demp]

in KHAN i TRUST!

[drrojas]

@1demp  better say "In KHAN WE TRUST"

[AllahCreatedMe]

@1demp In God first, then Khan.

[prusho90]

brilliant!..

[lohrite]

Well ,i couldnt understand for the stupid book.

I just searched this :)

Thanks Sal

Understood the Mean value theorem

[colombiano741]

Really Appreciate This Vid., Helped More Than You Think, Thanks

[uxxin]

excellent video : )

[jh8182]

This is the best

[twistc7]

You're the man where you live.

[SwampyOnNotes]

Sal inspires me.... Never thought i'd be able to understand calc until i started watching Sal's videos........

[mwtillotson]

First video I've seen from Khan. Such a great teacher.

[silkydude]

Great stuff man...

You have a gift....

thank you for sharing it with the world...

[madscirat]

Youve got it right Sal. Teachers assign far to much importance to obvious theorems with overcomplicated language and far to little to the sort of gut understanding which is your focus.

[nguyenkhan202]

Instructors sometimes used difficult equations to explain the theorem in stead of easy one like this on the vid.

[Antilli]

If only teachers could explain it like this. You're right, they always use difficult words to explain everything, while it's not needed. Sometimes I get the feeling they don't understand it themselves and are just repeating what they've been taught and forced into their brains.. Lol.

[abdullah57habib]

nice video! will check out more of yours soon

[saitothelegend]

Man! You actually made me want to learn Calculus again, nice job and wonderful clarity!

[BosnaChan]

Thank you man, you helped a lot!

[ElmTheWar]

I effing love you

[algaerancher21]

Great thank you

[TheHassanson1]

Hey Khan Big up on a job well done.

Could you please Post something on Rolle's Thereom.

[Sa20ni]

Thank you! I would have spent hours banging my head into the book, but you've made it very easy to understand :)

[varaprasad111]

amazing explanation

u made me love math

[cnx33]

can you please talk about the extreme value and intermediate value theorem?? :)

[ThePaddle4u]

wow, i was so confused and now this makes perfect sense! who needs a teacher, when i've got this guy!

[timtu22]

I hear that with the Nobel Prize. There should be a Prize for educating the masses for free. It is heroic.

[MonoFocus]

@timtu22 Actually The Khan Academy received the Microsoft Tech Award for Education in 2009 -- and I can't think of anyone who deserves it more than him :)

[timtu22]

So I've read! And certainly he deserves it. He is putting me through engineering!

[MonoFocus]

@timtu22 He has also helped me a gazillion times. My math books at the university tend to present things in a rather obscure way so it's wonderful to have Sal explain it in a pleasant, friendly, intuitive and totally down-to-earth way :)

[onlyAerik]

khanacademy needs us to social network the shit out of it.

[xwwz4wnn]

u r the best calculus teacher i've ever seen in my life

[surfmimibg]

I love you

You are saving us hundreds of dollars each day -fre education. You really should win a Nobel Prize since your more useful than anyone who has won this year!!

[cemdemo]

you simply rock.

[abood89tube]

You should get a Nobel prize :)

[gobberpooper]

lol before I would read my brother's calc textbook and then come here just so I could grasp the concept easier. That ended by the time I was finished with limits. Now I just come straight here and I've gone through a good chunk of the AP Calculus BC course within 3 days

[jacob12385]

man, i owe you my ENTIRE YEAR

[kabeer069]

thanks dude u made it look so easy i get it 100percent

[falidanfan]

Thank youuuuu!

[jponcik]

you helped me more than any calculus teacher ever has in my whole life

[doubleja]

Can someone tell me again, why I pay hundreds of dollars on books and for bullshit arrogant professors to kick me out of class for coming 2 min late to lecture?

[MichBich1234]

i think i will call it now and say, Sal is the most loved person on youtube.

[DemonPacman]

@MichBich1234 Him and PatrickJMT are pretty much the most awesome people on the internet.

[saturnv3]

Olive-Themed Windows XP?

Like a pro!

[dual85]

I don't even look at my book anymore. Whenever I get stuck I come right here.

[knmhb222]

@dual85

Same here!

[xfactordc3116]

Big Help. Thx

[BadBoyKing2009]

you rule

[add1c7i0n]

thanks homie

[Mikey041291]

Thanks lots. I understand it now. :]

[Pr0x1mo]

Wow dude, such a better explanation than my actual Calc book. Khan's videos, and my Calc for dummies book has made all the convolution and mathematical rhetoric so understandable. It's so much easier to figure out a problem when you understand the "why" of it, and you're not arbitrarily memorizing equations, symbols, and jargon.

[MrBucalemun]

Thank You !!! You've helped soo much.

[RylyC]

"I think this calls for magenta" laugh and learned!

[E3tiger]

@RylyC haha i loved that part!

[sponsoredwalk1]

After seeing this in my book for god knows how long and being dumbfounded you clarified everything in 16 mins, clearly. You should write a book in the exact same style as this presentation! I think you'd be the first person to do justice to the label on every single calculus text out there

"Ever since i picked up this book, i haven't been afraid of math class - M. Schlezinger - Wisconsin W.A" lol

[marcusjhung]

haha you're cough made me jump and drop my math book XD

[michalchik]

Are not all differentiable functions continuous?

[xlubnaax]

yeah they are.

[Superman550]

Not all continuous functions are differentiable though.

[michalchik]

Yes, i know, but he set two requirements, continuous and differentiable. Differentiable requires continuous so his first requirement is redundant.

[michellearobinson]

michalchik

The weakest hypotheses are that the function is continuous on the closed interval [a,b] and differentiable on the open interval (a,b). These two conditions are not redundant. There are functions that are differentiable on (a,b) but not even defined at a or b, or differentiable on (a,b) and defined at a and b, but not continuous at a or b (just re-define the function at a or b).

[ILUVFFANDKH]

well..if u have a cusp, vertical asymptote, and or cornor, those are discontinuities. so they will not be differentiable at those points (will have no derivatives) but u can have a specific interval that is continuos.

i hope that helps :)

[fzshinobi]

Making a pointless thing point-fully interesting, thanks.

[CubanLUVash]

THe best video, my teacher is so cocky and tries to explain things so confusing, doesnt relate to anything, it sucks, and he wonders why people do so bad in class.

[beastlt12]

Very clear video. Thanks for the good presentation.

[smugg13i2]

What I can say to you is "If you were a women i would make love to you." All your videos explains so much better than my 60 year old math teacher

[sjb167]

ROFL, that's hilarious bro but he would deserve it, so all you women out there, you know, that's something to keep in mind..

[unrealriot]

my calculus textbook has no examples of it, it just explains concepts and means nothing to solve my problem, but this video really helps, thanks.

[zdinath]

Calculus Textbooks are useless.

[chriskill08]

at the start of th video you said you were going to show a function that is continuous but not differentiable but did not do that

[jessicahd24]

y = |x| is continuous but not differentiable

[timo86m]

f(x)=|x|

f'(x)=sign(x) whatever that means

[korrisha]

wow why you were not my lecturer

[etarc345]

Wow, your clarity is staggering. Thank you, i feel much more prepared for the AP test thanks to you

[sebassucc]

sounds like your gonna fail

[etarc345]

I've passed every practice AP test we've taken. So I highly doubt I will fail. What I meant was more prepared was that I will have a better opportunity to get a 5.

[believescience]

have you done any IVT?

[dildeanum786]

I was really lost in calculus until I saw your Videos. Thank You so Much :)

[kingmeeko]

so good, my calc teacher really doesnt teach and doesnt try to so i really appreciate it. thanks again

[Zulu424]

you are a god damned idiot.

[iluvjiyongx3]

im not in calc now, but im pretty sure that i can handle it cuz of ur vids, thanks!!

[RedBishop81]

This was very helpful. I am reviewing for my midterm, and I had a basic grasp on the MVT, but now I feel much more confident in my understanding of the theorem. Thanks. (And many of your other videos are superb as well.)

[Irenerz]

WOW this really helped! thank you so much! :D

[dominik13579]

Thanx!!!

[AbyssZomG]

This was wonderful :-)

[peterragheb]

Good Job. thanks

[matingwarhawk]

infinitely better job than my own calc teacher thank you

[tritcher]

please, keep the videos comming! thanks so much

[sanabes]

thank you so much..... that was reallllly helpful

[owimevil]

you're absolutely great! thanks a lot. you helped me in college calculus a lot!

[VictimOfBoredom]

God, I hate to sound harsh, but my calc teacher ought to be fired! I wish I could just watch your videos instead of being required to attend a useless class. McCain and Obama are looking for the solution to getting America's public education on the right track - I think I've found it! Khan Academy for every student in the nation!

[bangalirussian]

aight homie u didnt do a bad job, it was aight.

[Ltyrann]

Sal,

Just want to point something out. According to the mean value theorem f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b), then there is at least one number c in the interval (a,b)

You stated many times that c could be any number between a and b and that it could even be a or b (time=07:07) wouldn't that go against the definition? of c being in the interval (a,b) meaning that it must be between a and b?

Thanks for the videos, they are of great help!!

[khanacademy]

You're right that there must be a c other than a or b, but f'(a) or f'(b) might also work (in the case of a line for example). I should have been more clear.

[Waranle]

Thank you alot Sam

[AkashP4]

Thank you Sal! It has been a great encouragement to me!